The present invention relates to a semiconductor structure including an on-chip inductor with frequency-dependent inductance, a semiconductor circuit for the same, and a design structure for the same.
On-chip inductors are used in semiconductor structures for analog applications. Frequently, on-chip inductors are employed with other semiconductor components to form a resonant circuit having a high Q factor. The Q factor, or the quality factor, is a metric of performance of a resonant system. The Q factor of a resonant system is given by 2π times the energy stored in the resonant system divided by energy loss per cycle. A resonant system with a high Q-factor is capable of holding the stored energy in the system for many periods of the oscillation frequency of the system.
On-chip inductors are typically formed as a set of at least one metal line within a back-end-of-line (BEOL) dielectric material layer stack. Since the BEOL dielectric material layer stack is employed to form other metal interconnect structures, such on-chip inductors may be formed employing standard semiconductor processing steps without employing additional processing steps or additional masks.
Skin depth effect on the surface of metal lines influences the inductance of on-chip inductors especially on high frequency operations. The skin depth δs of a metal in MKS unit system, i.e., in meters, is given by:
            δ      s        =                            2          ⁢          ρ                          2          ⁢          π          ⁢                                          ⁢          f          ⁢                                          ⁢                      μ            0                    ⁢                      μ            R                                ,wherein ρ is the bulk resistivity of the metal in Ohm-meters, f is the frequency of the electromagnetic radiation, μ0 is a permeability constant of vacuum which is 4π×10−7 Henries/meter, and μR is relative permeability, which is usually about 1.0 for most non-ferromagnetic materials. The skin depth δs is about 2 microns at about 1 GHz and about 0.2 microns at about 100 GHz for most highly conductive materials such as Au, Ag, Cu and Al.
Other than the skin depth effect, which causes the inductance of on-chip inductors to slowly decrease with frequency of the electrical signal in the on-chip inductor, the on-chip inductors have otherwise substantially frequency independent inductance. For practical purposes of circuit design, therefore, on-chip inductors may have only one target inductance value.
Many semiconductor circuits require, however, different values of inductance at different signal frequencies for optimal performance. In view of the above, therefore, there exists a need for a semiconductor structure including an on-chip inductor having a frequency-dependent inductance, a semiconductor circuit for the same, and a design structure for the same.